Determine how many solutions exist for the system of equations. ${-12x-3y = 3}$ ${12x+3y = -3}$
Explanation: Convert both equations to slope-intercept form: ${-12x-3y = 3}$ $-12x{+12x} - 3y = 3{+12x}$ $-3y = 3+12x$ $y = -1-4x$ ${y = -4x-1}$ ${12x+3y = -3}$ $12x{-12x} + 3y = -3{-12x}$ $3y = -3-12x$ $y = -1-4x$ ${y = -4x-1}$ Just by looking at both equations in slope-intercept form, what can you determine? ${y = -4x-1}$ ${y = -4x-1}$ Both equations have the same slope and the same y-intercept, which means the lines would completely overlap. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ Since any solution of ${-12x-3y = 3}$ is also a solution of ${12x+3y = -3}$, there are infinitely many solutions.